Assume that the traffic to the web site of Smiley's People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.58 million visitors per day and a standard deviation of 700,000 visitors per day. (a) What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits. 0.7549 (b) What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits. 0.9850 (c) What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits. 0.2167 (d) Assume that 85% of the time, the Smiley's People web servers can handle the daily web traffic volume without purchasing additional server capacity. What is the amount of web traffic that will require Smiley's People to purchase additional server capacity? If needed, round your answer to two dedimal digits. 5.25 million visitors per day
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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